A US Air Force U-2 jet takes off from the Royal Air Force base at Akrotiri in Cyprus, March 20. Western forces hit targets along Libya's coast, using strikes from air and sea to force Muammar Qaddafi's troops to cease fire and end attacks on civilians.

Combat jets from the US, France, and Britain today rule the skies over Libya. The forces of Libyan leader Muammar Qaddafi – battered by coalition air power – have retreated. Rebel fighters are regrouping and moving to retake ground recently lost.

What happens now?

Days after US military forces struck in a third recent conflict overseas, many in Washington remain uneasy about a Libya engagement whose objectives seem less than clear and that began as Mr. Qaddafi appeared on the verge of regaining his iron grip on the country.

US officials insist that the purpose of the Libya intervention is protection of civilians, per United Nations Security Council resolution. It is a humanitarian operation, they say, not a move to pick sides in Libya’s developing civil war.

That’s a point of view backed by surrounding Arab nations, who supported the initial strikes.

But some allies – notably France – have talked tougher and may push for an endgame that includes military cooperation with the rebels and Qaddafi’s ouster. For the Obama administration, managing diplomatic conflicts over Libya strategy may prove more difficult than managing warplanes in Libyan airspace.

On Monday, Pentagon officials said that the ad hoc coalition had effectively imposed a no-fly zone over Libya in the wake of weekend airstrikes. There were no indications, they said, that Libyan forces had attempted to fly any aircraft in recent hours.

“We judge these strikes to have been very effective in significantly degrading the regime’s air defense capability. We believe his forces are under significant stress and suffering from both isolation and a good deal of confusion,” said Navy Vice Adm. William Gortney, staff director for the Joint Chiefs of Staff, at a Pentagon news conference.

Gortney and other US officials said that Qaddafi himself is not a target of the aircraft enforcing the no-fly zone, despite a large explosion that hit his personal compound Sunday in the closing hours of the initial round of bombing.

The US clearly believes that the mandate of the UN Security Council resolution does not extend to direct attempts at regime change. But in the past, President Obama has called directly on Qaddafi to go. What happens if Qaddafi survives the next few weeks and the Libyan conflict hardens into a prolonged civil war? Will the US participate in a no-fly zone that stretches for years, as it did over Iraq in the wake of the 1990-91 Gulf War?

Would the US accept a cease-fire agreement that leaves Qaddafi in place? Would it look weak of it did?

“The credibility of the US policy hangs on the departure of Qaddafi, and right now that looks like far from a foregone conclusion,” says Professor Martel.

What happens if France pushes for an escalation in the airstrikes? After all, France has already recognized the opposition leadership, based in Benghazi, as the true Libyan government.

Yet Mr. Obama has ruled out use of US ground troops and spoken of an operation that lasts days, not weeks. And Arab League secretary-general Amre Moussa has publicly deplored the scope and intensity of military actions that have already taken place.

All this uncertainty has led to criticism of the operation from senior Republican lawmakers in Washington.

In a statement, House Speaker John Boehner said that the Obama administration “has a responsibility to define for the American people, the Congress, and our troops what the mission in Libya is” and how it will be accomplished.

On Sunday, former presidential candidate Sen. John McCain (R) of Arizona said that he hoped the no-fly zone had not come too late to prevent Qaddafi from regaining his power.

“Obviously, if we had taken this step a couple weeks ago, a no-fly zone would probably have been enough. Now, a no-fly zone is not enough. There needs to be other efforts made,” said Senator McCain on CNN’s “State of the Union.”